New convergence results for alternating methods |
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| Institution: | 1. Research Center for Science, Xi''an jiaotong University, People''s Republic of China;2. Department of Computer Science and Mathematics, Teacher College of Shanxi University, Taiyuan 030012, People''s Republic of China;3. Department of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, People''s Republic of China |
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| Abstract: | The alternating methods for solving the large system of linear equations Ax=b are investigated. The convergence and the monotone convergence theories for the alternating method are formulated when the coefficient matrix is an H-matrix or a monotone matrix. Sufficient conditions are established for the induced splitting by the alternating method to be a regular splitting. Furthermore, new comparison theorems which improve previous comparison theorems are proved and several concrete applications are given. |
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